Categorizing Approaches to the Cosmological Constant Problem Stefan Nobbenhuis Supervisor: Prof. G. ’t Hooft August 28th 2005 COSMO-05, Bonn. gr-qc/0411093

The Problem in Threefold Contribution to vacuum Energy! = -1 for CC 1) Unnatural values 2) Why not exactly zero? 3) Cosmic Coincidence Problem Contribution to vacuum Energy!

To curve vacuum spacetime costs a lot of energy, whereas stretching it, is (almost) for free… © Gerard ’t Hooft This is unusual, for most ordinary stuff, stretching it is much harder than curving it!

Type I: Symmetry Principle Type I: Symmetry Principle Type II: Backreaction SUSY Imaginary Space Energy  - Energy Conformal Symmetry Holography Sub/super-Planckian Other universes… Instabilities of dS-space Scalar field Gravitons RG-Group Running Trace Anomaly BH production Type 0: Just Fine-tuning 2) Beyond QM 1) Beyond 4D Type III: Violating Equivalence Principle Type IV: Statistical Distribution Anthropic Principle Discrete Continue Wavefunction of the universe Wormholes Massive Gravitons Ghost Condensation Graviton as Goldstone Boson Fat Gravitons

Symmetry Argument Supersymmetry Vanishing vacuum energy if SUSY is unbroken SUGRA In D = 2+1 the ground state can be exactly supersymmetric without supersymmetric excited states (Witten (1994)) Generically supercurrents are covariantly conserved: But in the presence of a covariantly constant spinor, a conserved current can be constructed and therefore a conserved supercharge: m However, in 2+1 dimensions, any mass m produces a conical spacetime at space infinity: no killing spinors exist!

Consider the following transformation: Imaginary space Consider the following transformation: So if we postulate this transformation as a symmetry, a CC-term is forbidden! A deeper reason could be a change of our boundary conditions. Normally we quantize a field by putting it in a box and impose periodic boundary conditions on its real coordinates.

What happens if we impose boundary conditions on imaginary parts? Re Positive energy particles transform into negative energy particles Main problem however, is that masses seem to be forbidden now: This results from ‘first’ quantization: Which explicitly violates the symmetry… Higgs Mechanism? 3+3 dimensional spacetime?

Modifications of General Relativity Infinite volume extra dimensions V(r) ~ 4D for r < rc ~ 5D for r > rc For N > 2, H decreases as  increases! For N > 2, solutions can be paramtetrized as:

Unclear whether it is viable! Infinite volume extra dimensions brane singularity yg However, the extra d.o.f., the ‘brane bending mode’ becomes strongly coupled, resulting in a breakdown of the effective theory: the physics becomes sensitive to the unknown UV completion of the theory. This is a much more general phenomenon, changing a theory in the IR by adding a new d.o.f. often leads to strong coupling of this d.o.f. in the UV. Reason here is that the new scalar has no kinetic terms, but does have cubic and higher order interactions terms. Unclear whether it is viable!

Conclusions So far none of the approaches stands out as a serious candidate for a solution Severeness fine-tuning seems to indicate to more than just a philosophical point No satisfactory symmetry principle available that can explain smallness of CC Supersymmetry does not seem to help If CC non-zero nowadays, a back-reaction mechanism might be favorable, but these generally are either too weak, or lead to inconsistencies. Near-future experiments will fortunately help end some speculations